Proposition 4  (cf. [1]}, Theorem 6.1.1)
Let \(X\)  be a Banach space with a Schauder basis \(\lbrace e_1,e_2,\ldots \rbrace \) , and \(Q\in M_{X}\)  and \(P_n:X\rightarrow X ~~(n\in \mathbb {N}\)  be the projector onto the linear span of \(\lbrace e_1,e_2,\ldots , e_n\rbrace \) . Then, we have
\({1\over a}\lim _{n\rightarrow \infty }\sup &\left(\sup _{x\in Q}\Vert (I-P_n)(x)\Vert  \right) \le \chi (Q)\\&\le \inf _{n}\left(\sup _{x\in Q}\Vert (I-P_n)(x)\Vert  \right)\le \lim _{n\rightarrow \infty }\sup \left(\sup _{x\in Q}\Vert (I-P_n)(x)\Vert  \right)\) 
